Most people stop listening once someone says the word math. They'll nod along in an attempt to hide their utter disdain for the topic. This book will guide you through the math needed for data science, specifically statistics and probability. We will use these subdomains of mathematics to create what are called models.

A data model refers to an organized and formal relationship between elements of data, usually meant to simulate a real-world phenomenon.

Essentially, we will use math in order to formalize relationships between variables. As a former pure mathematician and current math teacher, I know how difficult this can be. I will do my best to explain everything as clearly as I can. Between the three areas of data science, math is what allows us to move from domain to domain. Understanding the theory allows us to apply a model that we built for the fashion industry to a financial model.

The math covered in this book ranges from basic algebra to advanced probabilistic and statistical modeling. Do not skip over these chapters, even if you already know it or you're afraid of it. Every mathematical concept I introduce, I do so with care, examples, and purpose. The math in this book is essential for data scientists.

Example – spawner-recruit models

In biology, we use, among many others, a model known as the spawner-recruit model to judge the biological health of a species. It is a basic relationship between the number of healthy parental units of a species and the number of new units in the group of animals. In a public dataset of the number of salmon spawners and recruits, the following graph was formed to visualize the relationship between the two. We can see that there definitely is some sort of positive relationship (as one goes up, so does the other). But how can we formalize this relationship? For example, if we knew the number of spawners in a population, could we predict the number of recruits that group would obtain, and vice versa?

Essentially, models allow us to plug in one variable to get the other. Consider the following example:

In this example, let's say we knew that a group of salmons had 1.15 (in thousands) of spawners. Then, we would have the following:

This result can be very beneficial to estimate how the health of a population is changing. If we can create these models, we can visually observe how the relationship between the two variables can change.

There are many types of data models, including probabilistic and statistical models. Both of these are subsets of a larger paradigm, called machine learning. The essential idea behind these three topics is that we use data in order to come up with the best model possible. We no longer rely on human instincts, rather, we rely on data.

The spawner-recruit model visualized

The purpose of this example is to show how we can define relationships between data elements using mathematical equations. The fact that I used salmon health data was irrelevant! Throughout this book, we will look at relationships involving marketing dollars, sentiment data, restaurant reviews, and much more. The main reason for this is that I would like you (the reader) to be exposed to as many domains as possible.

Math and coding are vehicles that allow data scientists to step back and apply their skills virtually anywhere.

Let's be honest. You probably think computer science is way cooler than math. That's ok, I don't blame you. The news isn't filled with math news like it is with news on the technological front. You don't turn on the TV to see a new theory on primes, rather, you will see investigative reports on how the latest smartphone can take photos of cats better or something. Computer languages are how we communicate with the machine and tell it to do our bidding. A computer speaks many languages and, like a book, can be written in many languages; similarly, data science can also be done in many languages. Python, Julia, and R are some of the many languages available to us. This book will focus exclusively on using Python.

We will use Python for a variety of reasons:

The last is probably the biggest reason we will focus on Python. These prebuilt modules are not only powerful, but also easy to pick up. By the end of the first few chapters, you will be very comfortable with these modules. Some of these modules are as follows:

X = 5.8
Y = 9.5

X + Y == 15.3  # This is True!

X - Y == 15.3  # This is False!
5if x + y == 15.3:   # If the statement is true:
  print "True!"     # print something!

my_list = [1, 5.7, True, "apples"]

len(my_list) == 4  # 4 objects in the list

my_list[0] == 1    # the first object


my_list[1] == 5.7    # the second object

Here is some more Python code. In this example, I will be parsing some tweets about stock prices (one of the important case studies in this book will be trying to predict market movements based on popular sentiment regarding stocks on social media):

tweet = "RT @j_o_n_dnger: $TWTR now top holding for 
             Andor, unseating $AAPL"

words_in_tweet = first_tweet.split(' ') # list of words in tweet

for word in words_in_tweet:             # for each word in list
  if "$" in word:                       # if word has a "cashtag" 
  print "THIS TWEET IS ABOUT", word  # alert the user

I will point out a few things about this code snippet, line by line, as follows:

The output of this code will be as follows:

We get this output as these are the only words in the tweet that use the cashtag. Whenever I use Python in this book, I will ensure that I am as explicit as possible about what I am doing in each line of code.

As I mentioned earlier, this category focuses mainly on having knowledge about the particular topic you are working on. For example, if you are a financial analyst working on stock market data, you have a lot of domain knowledge. If you are a journalist looking at worldwide adoption rates, you might benefit from consulting an expert in the field. This book will attempt to show examples from several problem domains, including medicine, marketing, finance, and even UFO sightings!

Does that mean that if you're not a doctor, you can't work with medical data? Of course not! Great data scientists can apply their skills to any area, even if they aren't fluent in it. Data scientists can adapt to the field and contribute meaningfully when their analysis is complete.

A big part of domain knowledge is presentation. Depending on your audience, it can greatly matter how you present your findings. Your results are only as good as your vehicle of communication. You can predict the movement of the market with 99.99% accuracy, but if your program is impossible to execute, your results will go unused. Likewise, if your vehicle is inappropriate for the field, your results will go equally unused.